Duffing map

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Phase portrait of a two-well Duffing oscillator showing chaotic behavior
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Phase portrait of a two-well Duffing oscillator showing chaotic behavior

The Duffing map is a discrete-time dynamical system. It is an example of a dynamical system that exhibits chaotic behavior. The Duffing map takes a point (xn, yn ) in the plane and maps it to a new point given by

x_{n+1}=y_n\,
y_{n+1}=-bx_n+ay_n-y_n^3.\,

The map depends on the two constants a and b. It is a discrete version of the Duffing equation.

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